Naslov
Unavoidable collections of balls for isotropic Levy processes

Autori
Mimica, Ante ; Vondraček, Zoran

Izvornik
Stochastic processes and their applications (0304-4149) 124 (2014), 3; 1303-1334

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Isotropic Levy process ; Green function ; minimal thinness at infinity

Sažetak
A collection $\{; ; ; ; ; ; \overline{; ; ; ; ; ; B}; ; ; ; ; ; (x_n, r_n)\}; ; ; ; ; ; _{; ; ; ; ; ; n\ge 1}; ; ; ; ; ; $ of pairwise disjoint balls in the Euclidean space $\R^d$ is said to be avoidable with respect to a transient process $X$ if the process with positive probability escapes to infinity without hitting any ball. In this paper we study sufficient and necessary conditions for avoidability with respect to unimodal isotropic L\'evy processes satisfying a certain scaling hypothesis. These conditions are expressed in terms of the characteristic exponent of the process, or alternatively, in terms of the corresponding Green function. We also discuss the same problem for a random collection of balls. The results are generalization of several recent results for the case of Brownian motion.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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